I've been improving an algorithm which I call the B.U.T. technique (Bivalue Universal Transformation) to make sudoku puzzles. Then I added a mask, but it makes sudokus only when I allow clues to fill the WHOLE mask (never a partial subset of the mask).

One example is below. I call it the "B.U.T.-whole" sudoku because it was created with the B.U.T. algorithm and a whole mask: